シートを指定するだけで良いと思います。
Sheet2という名前ならこんな感じ。
Sub test()
　　Worksheets("Sheet2").TextBoxes.Delete
End Sub

返事が遅くなりすみません。
下記に、コードを記載します。

Sub sh_Copy()

ActiveSheet.Unprotect Password:="PASS"

Dim s As Shape
  For Each s In ActiveSheet.Shapes
    If Not Application.Intersect(s.TopLeftCell, Range("A1:N29")) Is Nothing Then
    If s.AutoShapeType = msoShapeOval Then
      s.Delete
    End If
    End If
  Next
  
Dim s1 As Shape
  For Each s1 In ActiveSheet.Shapes
    If Not Application.Intersect(s1.TopLeftCell, Range("A1:N29")) Is Nothing Then
    If s1.AutoShapeType = msoShapeRoundedRectangle Then
      s1.Delete
    End If
    End If
  Next
  
 Dim sht As Object
    For Each sht In ActiveWorkbook.Sheets
       sht.TextBoxes.Delete
    Next



Dim mySh As String

p1:
mySh = InputBox("いつの日程表を印刷しますか？" & Chr(13) & "　2017年1月　のように入力してください", "コピー先")
'Worksheets("印刷用").Range("A1:N29").Value = Worksheets(mySh).Range("A1:N29").Value

If mySh = "" Then Exit Sub



Worksheets(mySh).Range("A1:N29").Copy Worksheets("コピー先").Range("A1")




Range("L3").Clear
Range("J3").Clear



Dim s2 As Shape
  For Each s2 In ActiveSheet.Shapes
    If Not Application.Intersect(s2.TopLeftCell, Range("A1:N5")) Is Nothing Then
    If s2.AutoShapeType = msoShapeOval Then
      s2.Delete
    End If
    End If
  Next
  
Dim s3 As Shape
  For Each s3 In ActiveSheet.Shapes
    If Not Application.Intersect(s3.TopLeftCell, Range("A1:N5")) Is Nothing Then
    If s3.AutoShapeType = msoShapeRoundedRectangle Then
      s3.Delete
    End If
    End If
  Next

Worksheets("Sheet2").TextBoxes.Delete

ActiveSheet.Protect Password:="PASS"

End Sub

コードを見ただけですが、途中に
Dim sht As Object
    For Each sht In ActiveWorkbook.Sheets
       sht.TextBoxes.Delete
    Next
End Sub

とあるので、すべてのシートから削除されるのは
これがあるからと思います。